Question $1$:

$[30$ marks$]$

A centrifugal pump is used to pump water at $25C$ from a reservoir whose surface is $6\mathrm{.}1$ m above the centerline of the pump inlet. The piping system consists of $20\mathrm{.}574$ m of plastic pipe with an ID of $30\mathrm{.}48$ mm $.$ The length of pipe from the bottom of the lower reservoir to the pump inlet is $3\mathrm{.}6576$ m $.$ There are several minor losses in the piping system: a sharp$-$edged inlet $(K_L=0\mathrm{.}5),$ two flanged smooth $90$ regular elbows $(K_L=0\mathrm{.}3$ each$),$ two fully open flanged globe valves $(K_L=6\mathrm{.}0$ each$),$ and an exit loss into the upper reservoir $(K_L=1\mathrm{.}05).$ The pump's required net positive suction head is provided by the manufacturer as a curve fit: NPSH $=0\mathrm{.}3048m+1\mathrm{.}1486{10}^{-4}\frac{m}{L}p{m}^2{V}^{}{?}^2,$ where the volume flow rate is in Lpm$.$ The atmospheric pressure is $101\mathrm{.}325$ kPa and consider $=1$ and the volume flow rate $=151\mathrm{.}416\frac{L}{m}in$

a$)$ Estimate the actual NPSH and required NPSH$.$

b$)$ Could cavitation occur?

Check the picture and answer the question please